Solve. Write answers in standard form.

$$x^2+2 x+4=0$$

A rectangle is $4$ inches longer than it is wide and has an area of $165$ square inches. Find its dimensions.

Write $f(x)$ in the vertex form $f(x)=a(x-h)^2+k$, and identify the vertex.

$$f(x)=x^2+6 x-1$$

Solve. Write answers in standard form.

$$6 x-2 x^2=10$$

The table shows how irrigation of rice crops affects yield, where $x$ represents the percent of total area that is irrigated and $y$ is the rice yield in tons per hectare. ( 1 hectare $\approx 2.47$ acres.)

$$\begin{array}{|c|c|c|c|c|c|c|} \hline x & 0 & 20 & 40 & 60 & 80 & 100 \\ \hline y & 1.6 & 1.8 & 2.2 & 3.0 & 4.5 & 6.1 \\ \hline \end{array}$$

(a) Use least-squares regression to find a quadratic function that models the data.

(b) Solve the equation $f(x)=3$.7. Interpret the results.